Can anyone out there help me ?

Q1. The lengths of the diagonals of a rhombus are 16 cm and 12 cm respectively.Find the length of each of its sides.

Q2. The sum of two opposite angles of a 11gm is 130 degrees. Find the measure of each of its angles.

Let ABCD is a rhombus and AC and BD are the diagonals that intersect each other at O. AC = 16 cm ; BD = 12 cm

Since diagonals of a rhombus bisect each other at right angle, then

∠ AOD = 90⁰  and OA = OC = 8 cm ; OB = OD = 6 cm

Now, in Δ AOD ,

AD² = AO² + OD²

 = (8)² + (6)² 

 = 64 + 36

 AD²  = 100

AD = 10 cm 

So, each side of the rhombus is of 10 cm.

(2)

Let ABCD is a parallelogram.

∠ B + ∠ D = 130⁰ 

∠B + ∠B = 130⁰  ( Opposite angles of parallelogram are equal)

⇒∠B = 65⁰ = ∠D

Now, ∠B + ∠C = 180⁰  (Adjacent angles of parallelogram are supplementary

 ⇒  ∠C = 115⁰

Now, ∠A = ∠C = 115⁰  (Opposite angles of parallelogram are equal)